Bone Microdamage and Its Contributions to Fracture

Abstract

Microdamage formation is a major determinant of bone fracture. The nature and type of damage formed, as linear microcracks or diffuse damage, depends on the interaction between applied loading and the extracellular matrix. Human bone naturally experiences multi-axial cyclic loading. Changes in its extracellular matrix can contribute to the overall deterioration of bone’s mechanical integrity with aging and/or disease. This chapter provides a review of literature reports on the detection of microdamage and its limitations; alterations in microdamage with aging and disease; differences in microdamage between gender and bone’s two distinct structural forms (cancellous and cortical); and the role of microdamage in bone’s mechanical properties.

Appendix: Measurement of Bone’s Fracture Resistance

As mentioned previously, the fracture properties of bone can be altered drastically due to microdamage accumulation. These fracture properties include measures for strength (resistance to permanent deformation) and toughness (resistance to fracture) [7, 81]. In order to measure these properties, early studies on bone fracture utilized the strength-of-materials approach. The traditional method to measure strength in bone involves mechanical testing on un-notched specimens. This technique results in the initiation and propagation of fracture from random distribution of natural flaws. Evaluation of strength with this method is based on calculation of work-to-fracture (area under load-deformation curve) or the modulus of toughness (area under stress–strain curve). However, fracture resistance depends on the presence of preexisting defects (i.e. microdamage) in addition to the stress or stain applied to bone.

Hence, parallel research introduced a fracture mechanics based approach in which a controlled crack was induced in the specimen before mechanical testing in order to study bone’s fracture characteristics. The induced sharp pre-crack functions as the dominant flaw from which the crack initiates. Using a pre-cracked specimen, toughness at initiation and propagation can be measured. Initiation toughness (critical stress intensity factor [K_c] or strain energy release rate [G_c]) illustrates the inherent toughness of the bone whereas propagation toughness (slope of crack growth resistance curve) illustrates bone’s resistance to the propagation of a crack [82, 83]. For instance, compact tension specimens with an induced chevron notch have been successfully used for investigation of crack propagation and measurement of bone’s fracture resistance [62, 84]. The fracture mechanics approach has been recently been modified for application on small animal bones in order to measure whole bone toughness [82, 83]. Here, pre-cracked rodent long bones (e.g. femur) are mechanically tested via three-point bending. To calculate fracture toughness using this method, three-dimensional images obtained via microcomputed tomography can be utilized to pinpoint the exact location of the notch made in the bone. A cross-sectional image of the notch can then be imported into imaging software (e.g. ImageJ) to measure the inner and outer radii, cortical thickness, and notch angles (initial notch and notch at the instability region). If we assume that the test specimen can be approximated as an edge-cracked cylindrical pipe, these measurements as well as the load obtained during fracture can be incorporated to calculate the fracture toughness using Eq. (1):

$$ k = F_{b} *\frac{{P_{c} *S*R_{o} }}{{\pi (R_{o}^{4} - R_{i}^{4} )}}*\sqrt {\pi *\Uptheta } $$

(1)

where k = fracture toughness, P_c = maximum load (maximum load method) or load at fracture instability (instability method), S = span length, R_o = outer radius of cortical shell, R_i = inner radius of cortical shell, R_m = mean radius of cortical shell, Θ = half-crack angle at crack initiation (maximum load method) or half crack angle at fracture instability (instability method), t = cortical thickness, and F_b = geometrical factor for an edge-cracked cylindrical pipe. The geometrical factor is computed by Eqs. (2) through (8):

$$ F_{b} = \left( {1 + \frac{t}{{2R_{m} }}} \right)\left[ {A_{b} + B_{b} \left( {\frac{\Uptheta }{\pi }} \right) + C_{b} \left( {\frac{\Uptheta }{\pi }} \right)^{2} + D_{b} \left( {\frac{\Uptheta }{\pi }} \right)^{3} + E_{b} \left( {\frac{\Uptheta }{\pi }} \right)^{4} } \right] $$

(2)

$$ A_{b} = 0.65133 - 0.5774\xi - 0.3427\xi^{2} - 0.0681\xi^{3} $$

(3)

$$ B_{b} = 1.879 + 4.795\xi + 2.343\xi^{2} - 0.6197\xi^{3} $$

(4)

$$ C_{b} = - 9.779 - 38.14\xi - 6.611\xi^{2} + 3.972\xi^{3} $$

(5)

$$ D_{b} = 34.56 + 129.9\xi + 50.55\xi^{2} + 3.374\xi^{3} $$

(6)

$$ E_{b} = - 30.82 - 147.69\xi - 78.38\xi^{2} - 15.54\xi^{3} $$

(7)

$$ \xi = \log \left( {\frac{t}{{R_{m} }}} \right) $$

(8)

Comparison between the traditional and contemporary methods [82] shows that the notched technique produces smaller variations in fracture toughness than the un-notched method. Additionally, it was found that crack propagation properties measured from the controlled propagation of a crack due to a pre-crack more comprehensively captures the fracture behavior of bone [62]. As toughness measurements via this fracture mechanics based approach are dependent on applied loading, geometrical parameters, and a pre-machined notch (Fig. 7), this method improves the estimation of bone’s fracture resistance compared to that estimated by traditional methods [82, 83]. (Note that this differs from conventional methods in which the contributions of structural and material components to bone strength are not de-coupled.)

Fig. 7

Microcomputed tomography image of a mouse femur showing cortical thickness and endosteal and periosteal radii measured at three cross-sectional regions. Reprinted with permission from Elsevier [83]